Two-dimensional (2-D) boundary integral equation analysis of a notched circular microdisk resonator is presented. Results obtained provide accurate description of optical modes, free from the staircasing and discretization errors of other numerical techniques. Splitting of the double degenerate whispering-gallery (WG) modes and directional light output is demonstrated. The effect of the notch depth and width on the resonance wavelengths, Q factors, and emission patterns is studied. Further improvement of the directionality is demonstrated in an elliptical notched microdisk. Applications of the notched resonators to the design of microdisk lasers, oscillators, and biosensors are discussed.